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Kolmanovskii, V. and Myshkis, A. (1992) Applied Theory of Functional Differential Equations. Kluwer Academic Publishers Group, Dordrecht.
https://doi.org/10.1007/978-94-015-8084-7

has been cited by the following article:

• TITLE: Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets

  AUTHORS: Boubacar Sidiki Kouyaté, Modeste N’zi

  KEYWORDS: Vector-Borne Disease Epidemic Model, Stochastic Delay Differential Equations, Stochastic Stability, Lyapunov Functional Technique

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.1, January 31, 2024

  ABSTRACT: Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.